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# Standard #: MAFS.912.G-C.1.2 (Archived Standard)

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Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

### General Information

Subject Area: Mathematics
Domain-Subdomain: Geometry: Circles
Cluster: Understand and apply theorems about circles. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

### Test Item Specifications

N/A

Assessment Limits :
Items may include finding or describing the length of arcs when given
information.
Calculator :

Neutral

Clarification :
Students will solve problems related to circles using the properties of
central angles, inscribed angles, circumscribed angles, diameters,
Stimulus Attributes :
Items may be set in a real-world or mathematical context.
Response Attributes :
Items may require the student to use or choose the correct unit of
measure.

### Sample Test Items (1)

 Test Item # Question Difficulty Type Sample Item 1 In the diagram shown, chords AB and CD intersect at E. The measure of  is 120º, the measure of  is (2x)º, and the measure of  is (4x)º.What is the degree measure of ? N/A EE: Equation Editor

#### Related Courses

 Course Number1111 Course Title222 1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) 1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated)) 1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

#### Educational Game

 Name Description Tangled Web: An Angle Relationships Game You are a robotic spider tangled up in an angular web. Use your knowledge of angle relationships to collect flies and teleport through wormholes to rescue your spider family!

#### Formative Assessments

 Name Description Central and Inscribed Angles Students are asked to describe the relationship between a central angle and an inscribed angle that intercept the same arc. Tangent Line and Radius Students are asked to draw a circle, a tangent to the circle, and a radius to the point of tangency. Students are then asked to describe the relationship between the radius and the tangent line. Inscribed Angle on Diameter Students are asked to find the measures of two inscribed angles of a circle. Circles with Angles Students are given a diagram with inscribed, central, and circumscribed angles and are asked to identify each type of angle, determine angle measures, and describe relationships among them.

#### Lesson Plans

 Name Description The Seven Circles Water Fountain This lesson provides an opportunity for students to apply concepts related to circles, angles, area, and circumference to a design situation. Geometry Problems: Circles and Triangles This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: Solving problems by determining the lengths of the sides in right triangles. Finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches. Inscribing and Circumscribing Right Triangles This lesson is designed to enable students to develop strategies for describing relationships between right triangles and the radii of their inscribed and circumscribed circles. Seeking Circle Angles Students will start this lesson with a win-lose-draw game to review circle vocabulary words. They will then use examples on a discovery sheet to discover the relationships between arcs and the angles whose vertex is located on a circle, in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and questions answered on white boards. Seeking Circle Segments Students will start this lesson with a "Pictionary" game to review circle vocabulary terms. They will then use computers and GeoGebra to discover the relationships between portions of segments that intersect in the interior of the circle, and exterior to the circle. They will wrap up the lesson in a class discussion and consensus on rules (formulas).